You need to find the area of the the whole rectangle (including white region inside of it). Then subtract the white region from the whole area to get the area of the shaded region.
The area of the whole rectangle is
(9x - 2)(2x + 7)
= 18x^2 + 63x - 4x - 14
= 18x^2 + 59
The area of the white (unshaded) region is
3x(x + 12)
= 3x^2 + 36x
The area of the shaded region will be the area of the whole rectangle minus the area of the white region inside it.
(Area of whole rectangle) - (Area of unshaded region)
= (18x^2 + 59) - (3x^2 + 36x)
= 18x^2 + 59 - 3x^2 - 36x
= 15x^2 - 36x + 59
